Effect of different palatal expanders with miniscrews in surgically assisted rapid palatal expansion: A non-linear finite element analysis

ABSTRACT Introduction: Surgically assisted rapid palatal expansion (SARPE) has been the treatment of choice in subjects presenting skeletally mature sutures. Objective: The purpose of this study was to analyze stress distribution and displacement of the craniofacial and dentoalveolar structures resulting from three types of palatal expanders with surgical assistance using a non-linear finite element analysis. Material and Methods: Three different palatal expanders were designed: Model-I (tooth-bone-borne type containing four miniscrews), Model-II (tooth-bone-borne type containing two miniscrews), and Model-III (bone-borne type containing four miniscrews). A Le Fort I osteotomy was performed, and a total of 5.0 mm palatal expansion was simulated. Nonlinear analysis (three theory) method (geometric nonlinear theory, nonlinear contact theory, and nonlinear material methods) was used to evaluate stress and displacement of several craniofacial and dentoalveolar structures. Results: Regardless of the maxillary expander device type, surgically assisted rapid palatal expansion produces greater anterior maxillary expansion than posterior (ANS ranged from 2.675 mm to 3.444 mm, and PNS ranged from 0.522 mm to 1.721 mm); Model-I showed more parallel midpalatal suture opening pattern - PNS/ANS equal to 54%. In regards to ANS, Model-II (1.159 mm) and Model-III (1.000 mm) presented larger downward displacement than Model-I (0.343 mm). PNS displaced anteriorly more than ANS for all devices; Model-III presented the largest amount of forward displacement for PNS (1.147 mm) and ANS (1.064 mm). All three type of expanders showed similar dental displacement, and minimal craniofacial sutures separation. As expected, different maxillary expander designs produce different primary areas and levels of stresses (the bone-borne expander presented minimal stress at the teeth and the tooth-bone-borne expander with two miniscrews presented the highest). Conclusions: Based on this finite element method/finite element analysis, the results showed that different maxillary expander designs produce different primary areas and levels of stresses, minimal displacement of the craniofacial sutures, and different skeletal V-shape expansion.


INTRODUCTION
Maxillary transverse deficiency is one of the most common dental problems, and it has been reported in 7% of the American children population increasing to 9.5% of the American adult population. 1 To correct the transverse maxillary deficiency, maxillary expansion is a widely accepted procedure.Three treatment modalities are used today for maxillary expansion: rapid palatal expansion (RPE), slow palatal expansion (SPE), and surgically assisted rapid palatal expansion (SARPE).
To effectively correct a skeletal maxillary transverse deficiency, the expansion must maximize the skeletal effects while minimize the dental ones.The maxillary expansion is the treatment of choice for growing subjects, but for skeletally mature subjects the RPE and SPE have limited orthopedic effects.3][4][5] Therefore, SARPE has been the treatment of choice in subjects presenting skeletally mature sutures. 6e surgical approach releases the palatal plates from the circumpalatal sutures and offers a true orthopedic maxillary expansion. 6,7[10][11][12][13][14] Dental Press J Orthod.2024;29(1):e2423195 Regardless of the technique, with or without surgery approach, various maxillary expander devices have been used to promote palatal expansion.These devices can be categorized as toothborne, bone-borne, tooth-tissue-borne, and hybrid (combination of two types).It is important for the clinician to choose the best design and position of the maxillary expander device for the most desirable outcome. 15,16Recently, the use of miniscrew assisted rapid palatal expansion (MARPE) has increased the maxillary expander design armamentarium, and successful maxillary expansion with these expanders has been reported with minimum side effects to teeth and periodontium. 17,18though MARPE can promote midpalatal expansion in subjects presenting increased mechanical interlocking, SARPE is still preferred as the treatment in skeletally mature sutures due to predictability and stability. 19,20rious SARPE techniques were proposed, with the typical surgical procedure consisting of a Le Fort I osteotomy combined with corticotomy along the midpalatal suture.However, SARPE has shown inconsistencies in the midpalatal expansion pattern depending on the surgical technique and/or expander device design.The literature has reported more anterior dental expansion than posterior, 12,21 approximately parallel, 12,[22][23][24] or more posterior than anterior dental expansion. 25Other complications such as asymmetric expansion between the right Dental Press J Orthod.2024;29(1):e2423195 and left maxillary shelves have been reported. 20So, the dental and skeletal effects of different expanders and the stress distribution of the force used to promote maxillary expansion in the craniofacial structure still needs a better understanding.
It is known that the biomechanical response of bone under orthopedic forces, such as maxillary expansion, is complex.
To study stresses, strains, and displacements, finite element method and finite element analysis (FEM/FEA) was introduced to medical field. 26This type of analysis had made it possible to accurately evaluate the biomechanical components of living structures in a non-invasive manner that can barely be measured in vivo. 27,28With the help of FEA, the amount of displacement occurring in the maxilla and the change in the stress occurring in the surrounding structures can be evaluated.In order to make FEM/FEA a clinically applicable tool, the image acquisition, the material properties, the model, and the analysis should be robust and accurate.In addition, a non-linear analysis is essential (non-linear FEM/FEA is more powerful algorithm and addresses problems that linear FEM/FEA does not). 28To closely mimic the in-vivo outcome, this study evaluates the stress, the strain, and the displacement of the craniofacial structures after a total of 5 mm activation under SARPE using non-linear solution.
Dental Press J Orthod.2024;29(1):e2423195 The aim of this study was to compare the amount of displacement and stress distribution due to number of screws and different anchoring screw location of three different types of expansion appliance (bone-borne and hybrid) used in surgically assisted rapid palatal expansion on craniofacial and dentoalveolar structures using finite element analysis (FEA).The null hypothesis was that different expansion appliances do not change the pattern of maxillary expansion in a skeletally mature subject.

MATERIAL AND METHODS
A finite element model was generated using an anatomical model of a 22-year-old adult male obtained from an anatomagraphic database developed from magnetic resonance imaging (MRI). 29ch image of the head featured a slice thickness of 2.00 mm (256 x 256 x 240 mm) and additional anatomical segmentations were introduced in the original data. 30,31The Committee for the Protection of Human Subjects (CPHS) of the University of Texas Health Science Center at Houston reviewed the submission and determined it does not meet the regulatory definition of human subjects research (HSC-DB-23-0712).
All head bones (cranial vault, cranial base, and facial bones) and teeth were in STL format downloaded and merged using ANSYS Workbench software (19.2, ANSYS Inc. Houston, PA, USA).For the finite element analysis (FEA), a symmetrical model of the craniofacial and maxillofacial structures with the maxilla, teeth, and periodontal ligaments was created independently and included in the overall model.[34] In the scenario of this study, the expansion device designs (bone-borne palatal expander and hybrid expander), the number of mini-screws, and the mini-screw placement site were different.
Mimics software (version 15.0; Materialise, Leuven, Belgium) was used to edit and generate the final model.The offset command was used to model the periodontal ligament (PDL) with a thickness of 0.20 mm. 32Anisotropic materials were cortical and cancellous bone, periodontal ligament and homogeneous and isotropic materials were considered tooth and stainless steel.[34]

Material properties
Elastic modulus (Mpa) Poisson's ratio Shear modulus (Mpa)    Frictionless contact was defined between the maxillary surfaces separated by lateral osteotomy.Bonded contacts were defined between the teeth, the periodontal ligament and the screw of the expansion appliance and the maxilla.They move as a single unit, with no sliding or separation of faces and edges permitted.The amount of rotation of the maxilla was measured from angular changes made by the line passing through the nodes between anterior nasal spine (ANS) and posterior nasal spine (PNS) points with respect to the symmetrical plane of the skull.

FINITE ELEMENT MODEL
Quadratic tetrahedral elements were used for volumetric mesh generation the symmetric model, only the expansion device and the anchor screw are divided into quadratic hexahedral elements mesh structure.The FEA model was composed of 2,186,123 nodes and 1,462,604 elements, and the maxilla contained more fine elements than elsewhere of the skull.3][34] The mesh structure is given in the figures where we share the displacement and stress results.
Mesh convergence was performed to validate the solution and to show that the measured values do not vary with element size.The best number of elements was established in the model for the mesh convergence.
Mesh refinement was performed on the contact surface of the maxilla and sphenoid bone, in the area where the mini-screw was placed, and on the first molar tooth and its PDL.while Model-I presented the smallest (0.080 mm).In regards to   Median and lateral osteotomies were made in all models without pterygomaxillary suture separation.In all models, rotation and tipping of the maxilla were observed during expansion (Table 3).The wedge-shaped expansion pattern was observed in all models, but it was more prominent in It is important to notice that PNS and ANS presented the lowest von Mises stress values of the evaluated skeletal landmarks (Table 4).PNS stress distribution ranged from 0.015 MPa

DISCUSSION
Regardless of the maxillary expander device type, SARPE produces greater anterior maxillary expansion than posterior.
Although the V-shaped opening shape, the appliance design influences the skeletal and dental maxillary expansion pattern.Model-I showed less accentuate and the Model-II more accentuate V-shaped (PNS/ANS proportion of 54% and 20%, respectively).The skeletal V-shaped expansion pattern has been reported in other FEM/FEA studies regardless of the osteotomy technique. 12,21Clinical studies have also reported a V-shaped opening of the midpalatal suture due to SARPE. 13,24,36,37mparisons are problematic due to study design, surgical technique, and appliance design and position.In addition, it has been shown that age is also directly related to the opening pattern of the midpalatal suture, with older subjects presenting smaller and lesser parallel maxillary expansion. 38The anteroposterior position of the expander device can also influence the maxillary V-shape expansion. 15,21It is important for the clinician to choose the best design and position of the maxillary expander device according to the desirable outcome. 15RPE produces vertical skeletal displacement of the maxilla.
Based on ANS and PNS, SARPE displaced the maxilla downward more in the anterior than in the posterior.The more pronounced inferior than superior displacement of the maxillary complex was previously reported before in FEM/FEA and clinical studies, regardless of the surgery technique. 12,13,36The pattern of maxillary expansion and displacement after SARPE is probably due to the remaining attachments of the maxilla superiorly to the craniofacial bones, which produce a greater amount of resistance against expansion at the upper segments of the maxilla. 39 general, SARPE provides a similar pattern of dental displacement regardless of the expander device design.Dental structures such as central incisors presented downward and more lateral displacements, whereas the structures such as molars presented upward and less lateral displacement.Dental displacement pattern due to SARPE has shown inconsistencies according to surgical technique and/or expander device design, and more anterior dental expansion than posterior, 12,21 approximately parallel, 12,[22][23][24] and more posterior than anterior dental expansion, 25 have been reported by the literature.In addition, the V-shaped separation of the maxillary halves provides teeth displacement to not follow the same amount or direction of the skeletal base.The literature has demonstrated rotation of the maxillary segments after SARPE with or without pterygomaxillary distraction. 19,40The area closer to the fulcrum expe- of the dental and/or skeletal anchorage has influence on pterygoid plates. 15,41,45,46In growing subjects, minimal displacement of the pterygoid plates has been reported using FEM/FEA. 47It seems that the surgical technique could play important role on pterygoid plates displacement, 39,48,49 but surgeons are concerned about of the advantages of the pterygomaxillary disjunction due to the increasing of fractures in adjacent bones or injuring the vasculature in the posterior of the maxilla. 22fferent maxillary expander designs produce different primary areas and levels of stresses.As expected, the bone-borne device presented minimal stress at the teeth (maxillary first molars) and the tooth-bone-borne two miniscrew expander device presented the highest stress level on the anchor teeth.
Medial and lateral pterygoid plates are the skeletal area presenting the highest level of stress, with the Model-I presented approximately twice and thrice the stress of the Model-III and Model-II, respectively.,50 In general, craniofacial sutures stress dissipation follows from outside to inside and from superior to inferior with the structures connected to the cranium base exhibiting more stress level, 45 and our study corroborates in showing similar trend with very few exceptions.Some authors mentioned that the osteotomies are more important in reducing stress in certain areas than the type of the device. 48,49[50][51] In this study, the miniscrews were placed in safe and stable areas of the palate determined by clinical studies.As aforementioned, several factors such as patient's age, gender, type of expansion appliance design, miniscrew placement site, mid palatal suture maturity, bone density, and the response of muscles and soft tissues may affect the amount of expansion and success rate.Some of these factors (boundary conditions) 4] Koç O, Koç N, Jacob HB -Effect of different palatal expanders with miniscrews in surgically assisted rapid palatal expansion: A non-linear finite element analysis

28
Dental Press J Orthod.2024;29(1):e2423195 An important consideration in FEA studies is the reliability of the results and the repeatability of the analysis.52,54 The mesh structure has a direct impact on the accuracy of the solution and the results.The number of elements required in the model is found by mesh convergence.
52,56 In the analysis, it is not desired that the results change with changes in the mesh size.
The skewness mesh metrics spectrum (Fig 6) is important for a better understanding of the study's mesh quality.Low orthogonal quality and high skewness values are not recommended; 55 these values influence the accuracy of the analysis results, and the accuracy decreases as the average skewness value progresses from excellent to good.The mean mesh convergence value and skewness element quality of our model were excellent for all parts that make up the geometry.Previous FEM/FEA studies used incomplete and no-smooth geometric models, and did not specify mesh, mesh convergence, element size,   Stress on teeth can be associated to tipping, which can lead to potential tooth and surrounding tissue damage, and pain response.Ideally, maxillary expansion should maximize dentofacial orthopedics with minimal orthodontic tooth movement.
To avoid high stress on teeth, orthodontists should make use of bone-borne (Model-III) or tooth-bone-borne with four miniscrews (Model-I), which present not only more skeletal anchorage but also more posterior miniscrews (closer to the maxillary center of resistance).When periodontal health is doubtful, the bone-borne maxillary expander (Model-III) should be elected.
These SARPE-FEM/FEA simulation results may be helpful and instructive for the clinical application, but in-vivo studies are required to confirm these results.

LIMITATIONS
Clinical conditions are difficult to apply and standardize on a single patient with the same clinical characteristics as the patient who was used to generated the FEM/FEA for this study.
Additionally, the resistance of tooth movement may vary as the root approaches the cortical bone, and some areas of stress could be different.In this FEA simulation, relapse after expansion, bone remodeling, effects of soft tissues, muscles and chewing forces were not included in the analysis.The accuracy of the simulation should increase if these factors could be added to the boundary conditions.Therefore, the displacement and stress values may be higher than the clinical values and our findings could differ from clinical results.The highest stress value observed were in the pterygomaxillary suture and miniscrew insertion areas, and the maximum stress values occurring were extremely high.These values, which were a function of the FEM/FEA process (in a few elements of the volume and nodes components of the pterygomaxillary suture and miniscrew region) did not affect the results.55,57 In addition, the maximum stress value does not actually accumulate at a single point as in the analysis result, due to the flexibility of the bone against loads and its self-healing feature.

CONCLUSIONS
Based on finite element method/finite element analysis, the results of this surgical assisted rapid palatal expansion study reject the null hypothesis because there is a slightly different maxillary expansion pattern in a skeletally mature subject due to expander device design.In addition, the following conclusions can be drawn: » SARPE produces greater anterior than posterior maxillary expansion pattern regardless of the maxillary expander design, but the V-shaped expansion is less noticeable with the four mini-screw tooth-borne expander design.
» There is a vertical skeletal displacement of the maxilla due to SARPE.
» Maxillary expansion with to SARPE produces minimal displacement of the craniofacial sutures.
» Different maxillary expander designs produce different primary area and level of stresses.
» With the exception of the miniscrew area, the highest stress levels were measured in the medial and lateral pterygoid plates.

Figure 1 :
Figure 1: Three different palatal expander appliances design: Model-I is a tooth-bone-borne expander with four miniscrews placed 4 mm lateral to midpalatal suture (A), Model-II is a tooth-bone-borne with two miniscrews placed at the third rugae area (B), and Model-III is a bone-borne with four miniscrews placed 8 and 10 mm from the midpalatal suture (C).Screws were moved 2.5 mm in a transverse ( Z-axis ) direction ( 5 mm in total ).
Koç N, Jacob HB -Effect of different palatal expanders with miniscrews in surgically assisted rapid palatal expansion: A non-linear finite element analysis 10 Dental Press J Orthod.2024;29(1):e2423195means of the appliance arms; this expander was also located at maxillary first molar level.Model-III is a bone-borne palatal expander type design presenting four miniscrew expander (two anterior miniscrews placed 6.00 mm and the two posterior miniscrews placed 8.00 mm from the midpalatal suture, respectively); the expander was located at maxillary second premolar level.For standardization, regardless of the palatal expander type, the miniscrews were modeled with ANSYS Workbench software presenting the same sizes (1.60 mm diameter and 10.00 mm length).After creating the structures and appliances, a LeFort I osteotomy without pterygomaxillary suture osteotomy was performed in all models.In the simulation of the palatal expansion, the expander was moved transversely 2.50 mm, implying a total of 5.00 mm.Several dental and skeletal landmarks were incorporated in this study.Dental landmarks were: central and lateral incisors, canine, first and second premolars, and first and second molars; skeletal landmarks were: anterior nasal spine (ANS), posterior nasal spine (PNS), frontomaxillary suture, zygomaticomaxillary suture, frontozygomatic suture, zygomatic arc, medial pterygoid plate, lateral pterygoid plate.The foramen magnum was accepted as the stable point as it was completely fixed and stable.33Also, rotation and tipping of the maxilla were measured in all three planes.BOUNDARY CONDITIONSThe displacements of the aforementioned craniofacial structures were evaluated along X, Y, and Z coordinates against the transverse displacement of palatal shelves.The X-axis evaluated the changes in the anteroposterior plane, the Y-axis evaluated the changes in the vertical plane, and the Z-axis evaluated the changes in the transversal plane.Areas of stress were evaluated with the help of a different color scale band gap.Positive or negative values in the column of stress spectrum indicate tension or compression, respectively.A time-dependent transient structural (dynamic) type of analysis was used to evaluate the Von Mises stress distribution and the amount of displacement.An analysis solution was performed using nonlinear geometric theory (large deformations), nonlinear contact theory (frictionless) and nonlinear material theory (anisotropic).By using the measurement probe, displacement and stress values were measured on the same element in all models with ANSYS Workbench software.In all models, the displacement movement was transmitted to the maxilla with the help of miniscrews and the expansion screw was activated by 0.25 mm.In the symmetrical FEA model, transverse displacement of 2.50 mm was achieved in the Z-axis corresponding to 5.00 mm of movement.Results were obtained after a total activation of the expansion screw of 5 mm.Dental Press J Orthod.2024;29(1):e2423195

Koç O , 1 Figure 2 :
Figure 2: Displacement of the landmarks due to SARPE after 5 mm activation of the expander apparatus.Occlusal view simulation of the Model-I (A), Model-II (B), and Model -III (C), and frontal view simulation of the Model-I (D), Model-II (E), and Model -III (F).

Koç O ,
Koç N, Jacob HB -Effect of different palatal expanders with miniscrews in surgically assisted rapid palatal expansion: A non-linear finite element analysis 17 Dental Press J Orthod.2024;29(1):e2423195 Transversely, all models present lateral movements of the landmarks (Fig 2 and Table 3).As expected, anterior dental areas showed larger amounts of separation than posterior dental areas.Model-I and Model-III experienced over four mm (4.194 mm and 4.361 mm, respectively) of transverse movement for the central incisors whereas Model-II experienced 3.411 mm.Second molars presented more transverse movements on Model-I (2.668 mm) followed by Model-III (1.681 mm), and Model-II (1.315 mm).ANS also separated more than PNS, with Model-I presenting more parallel separation.Craniofacial sutures showed minimal transverse changes; zygomaticomaxillary suture showed the highest values ranging from 0.036 mm (Model-II) to 0.201 mm (Model-I).The medial pterygoid plate showed the highest amount of transverse displacement (0.896 mm for Model-I, 0.153 mm for Model-III, and 0.140 mm for Model-II) than the lateral pterygoid plate (0.216 mm for Model-I, 0.044 mm for Model-III, and 0.038 mm for Model-II).

DentalFigure 3 :
Figure 3: Stress distribution values for craniofacial structures including the miniscrew sites for Model-I expander type after 5 mm activation of the expander apparatus.(A) Sagittal view, (B) Coronal slice view showing the pterygomaxillary suture, (C) Axial view, and (D) Axo-posterior view.Highest stress area is presented in red.

(Figure 4 :DentalFigure 5 :
Figure 4: Stress distribution values for craniofacial structures including the miniscrew sites for Model-II expander type after 5 mm activation of the expander apparatus.(A) Sagittal view, (B) Coronal slice view showing the pterygomaxillary suture, (C) Axial view, and (D) Axo-posterior view.Highest stress area is presented in red.
riences less expansion, and the hemimaxillae are displaced transversely, with more expansion of the inferior part. 40Koç O, Koç N, Jacob HB -Effect of different palatal expanders with miniscrews in surgically assisted rapid palatal expansion: A non-linear finite element analysis 25 Dental Press J Orthod.2024;29(1):e2423195 Maxillary expansion due to SARPE produces minimal displacement of the craniofacial sutures.Most (81%) of the craniofacial suture measurements presented sutural displacement smaller than 0.5 mm.The largest craniofacial sutural displacement was promoted by the Model-I type device (slightly over 1.0 mm of vertical displacement of the frontomaxillary, zygomaticomaxillary, and frontozygomatic sutures).Rapid palatal expansion with and without surgical assistance have also shown minimal displacement of craniofacial sutures. 41It has been suggested that the resistance of transverse maxillary expansion is the zygomaticomaxillary buttress and the pterygomaxillary junction, 19 and eliminating the resistance to lateral movement by osteotomy should allow for larger maxillary basal bone movement. 43Maxillary expander design influences the transversal displacement of medial and lateral pterygoid plates.Maxillary expanders more posteriorly inserted, such as Model-I, showed considerably more vertical and lateral displacement of the medial and lateral pterygoid plates.Literature has shown maxillary expansion resistance by the pterygoid plate, 44 but the displacement of the pterygoid plates or zygomatic buttress has been controversial.Again, comparisons are problematic because the studies design, but the anteroposterior position

Koç O , 26 Dental
Koç N, Jacob HB -Effect of different palatal expanders with miniscrews in surgically assisted rapid palatal expansion: A non-linear finite element analysis

Table 1 :
Finite element model's material properties.

Table 2 :
Finite element model's element, nodes, mesh size and average skewness element quality convergence values.

Table 3 :
Unilateral displacements (mm) of the evaluated landmarks after 5 mm of the maxillary expander activation.

Table 4 :
The mean elemental stress (von Mises stress and first principal stress) distribution of the evaluated structures after 5 mm of the maxillary expander activation.

Koç O, Koç N, Jacob HB -Effect of different palatal expanders with miniscrews in surgically assisted rapid palatal expansion: A non-linear finite element analysis Dental Press J Orthod. 2024;29(1):e2423195
III in all the evaluated sutures, which is important in selecting this type of maxillary expansion appliance.Clinically, maxillary expansion has been reported to be more predictable under bone-borne maxillary expanders than tooth-borne expanders in growing patients.58Inaddition,when compared to multipiece Le Fort, SARPE produce less skeletal changes.59 Dental Press J Orthod.2024;29(1):e2423195 ferent types of (tooth-born, bone-born and hybrid) expansion appliance and anchor screw positions.Dental Press J Orthod.2024;29(1):e2423195 Dental Press J Orthod.2024;29(1):e2423195